统计与数据科学学院知识库

       置信区间展现的是剧兴趣参数的直实值落内测量结果的周围的程度，其给出的是感兴加参数的测量值的可信程度，置信区问是统计推明中的一个重要方向，因为估计山置信区同是我们进行预测的一个前提。对手不同的续计模型用运用的区间估计方法也量不相同的。在许主领域中，Bootstrap成为一种数据处理的有效方法，根多情况下，模型中感兴圆的静数的置信区间难以构建，为了解决这一问题，本文基于一类loottrop置信区向的估计方法，重新构建贝叶斯Bootatrap置信区间，分别研究在曲性回归模型以及分层代性回归模型的Bootstrap参数估计方法，并做了蒙特卡洛模拟比校和实证分析，比较分析了几种方法的优缺点。

       首先介绍了Bootstrap的一般估计问题，然后在一央新的置信区间的基础上，结合Bootstrap方法，构造Bootstrap置信区间和贝叶期Bootstrap置信区间，蒙特卡洛模拟结果显示:贝叶斯Bootstrap方法和Bootstrap方法能较好的保证覆盖率在名义置信水平，贝叶斯Bootstrap方法在保证覆盖率的同时，比Bootstrap方法有更高的稳定性，而经典方法在一般小样本量下覆盖率较低，同时平均区间长度过长，更不稳定，鉴于贝叶斯Bootstrap置信区间的优良表现，在实际应用中可以推荐使用贝叶斯Bootstrap作为一种很好的估计方法，

       其次是针对线性模型中感兴趣参数的估计问题，结合传统Bootstrap方法，提出了一种特殊的误差方整Bootstrap估计方法。在一定假设条件下，通过蒙特卡洛模拟，得出在样本量较小的情况下，误差方差Bootstrap估计方法和Bootstrap方法均优于传峡估计方法，当样本量较大的情况下，误差方差Bootstrap和Bootstrap方法，在精确性上公略微优于最小二乘估计方法

       然后是针对分层线性模型中感兴他参数的估计问题，采用蒙特卡洛模拟比较了传统统计方法，参数Bootstrap在分层战性模型中的表现。结果表明在分层此性模型的基础下以及小样本的情况时Bootstrap方法总体忧于传统统计方法。

       最后是案例分析，分别运用了两个例子来对Bootstrap进行了说明，一个对人口老龄化进行了分析预测，另一个对冠状病事进行了Bootstrp预测。

he confidenee interval shows the degree to which the true value of theparameter of interest falls around the measurement result, and gives the conidencedegree of the mcasured value of the paramcter of interest. The confidence interval isan important direction in statistical inference, because estimating the confidenceinterval is a prerequisite for our prediction.Interval estimation methods are alsodiffierent for diferent statistical models.In many areas, Bootstrap become a kind ofeffective method of data processing. in many cases, the confidence interval ofparameters of interest in the model is difficult to build., in order to solve this problem,this article is based on a class of Bootstrap confidence interval estimation method,rebuilding the bay leaf, Bootstrap confidence interval, respectively in the linearregression model and Bootstrap parameter estimation method of hierarchical linearregression model, and do the Monte Carlo simulation comparison and empiricalanalysis, comparative analysis the advantages and disadvantages of several methods.

Bootstrap general estimation problem are introduced first, and then on the basisof a new class of confidence interval, in combination with Bootstrap method,construct Bootstrap confidence interval and bay lcaf, Bootstrap confidence interval,Monte Carlo simulation results show that the bay leaf Bootstrap method andBootstrap method can better guarantee coverage in the name of the confidence level,bay leaf, Bootstrap method at the same time of guarantee coverage, higher stabilitythan Bootstrap method;However, the classical method has a low coverage rate with agenerally small sample size, and the average interval length is too long and moreunstable.Considering the excellent performance of bayes Bootstrap confidenceinterval, it is recommended to use bayes Bootstrap as a good estimation method inpractice.

Secondly, a special error variance Bootstrap estimation method is proposed toestimate the paramcters of interest in lincar models,Under certain assumptions andthrough monte carlo simulation, it is concluded that Bootstrap estimation method andBootstrap estimation method of error variance are better than traditional cstimation method in the case of small sample size.When the sample size is large, the errorvariance Bootstrap and Bootstrap method are slightly better than the least squarecstimation method in accuracy.

Then, Monte Carlo simulation is used to compare the performance of traditionalstatistical method and parameter Bootstrap in hierarchical lincar model.The resultsshow that the Bootstrap method is superior to the turaditional statistical method on thebasis of the hierarchical linear model and in the case of small samples.

Finally, Case Analysis was carried out to cxplain Bootstrap by using two subsetsrespectively. One was used to analyze and predict population aging, and the other wasused to predict coronavirus.